Analog multiplier including a time average integrating unit



United States Patent 3,517,880 ANALOG MULTIPLIER INCLUDING A TIMEAVERAGE INTEGRATING UNIT Thomas J. Hutton, Swissvale, Pa., assignor toWestinghouse Air Brake Company, Swissvale, Pa., a corporation ofPennsylvania Filed Aug. 1, 1968, Ser. No. 749,407 Int. Cl. G06g 7/16 US.Cl. 235-194 10 Claims ABSTRACT OF THE DISCLOSURE This invention relatesto an improved analog multiplier for multiplying at least first andsecond variables and ineludes in combination an amplifier, a gate, atime average integrating means, and a comparator. The amplifier has aninput which is the first variable, as well as an output. The timeaverage integrating means is electrically connected to the amplifier byway of the above-noted gate. The comparator has first and second inputs.The first input is a reference signal and the second input is equal tothe second variable. The comparator also has an output which controlsthe aforementioned gate, the output from the comparator appearing onlywhen the absolute value of the second variable is greater than theabsolute value of the reference signal. Accordingly, the time averageintegrating means integrates the amplifiers output to providemultiplication of the first and second variables.

My invention relates to an improved analog multiplier.

More specifically, my invention relates to an improved analog multiplierfor multiplying at least first and second variables and including incombination an amplifier, a gate, a time average integrating unit and acomparator. The above-noted amplifier has an input which is the firstvariable to be multiplied, as well as an output.

The time average integrating unit is electrically connected to theamplifier output by way of the above-noted gate.

The comparator has first and second inputs. The first input is areference signal and the second input is equal to the second variable.The comparator also has an output which controls the aforementionedgate, the output from the comparator appearing only when the absolutevalue of the second variable is greater than the absolute value of thereference signal. Accordingly, the time average integrating unitintegrates the amplifiers output to provide the multiplication of thefirst and second variables.

In railroad classification yards, there are many parameters that must beascertained such as, curved-track rolling resistance, straight trackrolling resistance, train velocity, etc. For example, an equation suchas the following must be solved in order to determine train velocity atthe foot of the classification yard hump:

el-c2 el-c2] (V02) 2 01) +29-9D 1- 2 m where,

3,517,880 Patented June 30, 1970 ice In large classification yards, adigital computer which may cost on the order of $100,000 is usually usedto make such calculations for the values of e cl) cl-c2 and and thussolve the equation. However, for relative small classification yards theuse of such elaborate, costly equipment to compute the products whichresult from the multiplication of each of the terms of the equationwould be totally out of the question for this would be a solution to aproblem that would be much like killing a fly with a Sledgehammer. Itwould therefore be much less costly to use an inexpensive analogmultiplier which possesses reasonable accuracy to calculate productssuch as those above noted in the smaller classification yards.

In the past small classification yards employed a servomechanism of thepotentiometer type where the two variables to be multiplied arerespectively represented by a potentiometer winding which bears a directrelation to one of the variables and the arm of which is moved as afunction of the second variable by a servo-motor. Since this arrangementis electromechanical in nature, this prior art approach is susceptibleto mechanical failure as well as inaccuracy due to inherent hysteresiserror in the servo and mechanical components. Also, there may bedifficulty in multiplying a third variable by the first two. Thus, whilethe dimension of the problem has been reduced, the solution to theproblem of accurate multiplication still leaves vast room forimprovement.

It is therefore an object of this invention to provide an analogmultiplier which will accurately multiply two or more variables by theemployment of an amplifier which has one of the variables as its inputin combination with a gate, and a comparator having two inputs, thefirst being a reference signal input, the second being the secondvariable, as well as a time average integrating means.

Another object of this invention is to provide an analog multiplierwhich can be completely eletcronic in nature.

Yet another object of this invention is to provide a virtuallyinstantaneous multiplication of two variables by the employment of solidstate electronic components.

Still another object of this invention is to provide an analogmultiplier which is compact and inexpensive.

In the attainment of the foregoing objects an analog multipler has beeninvented for multiplying at least a first and second variable whichincludes in combination therewith an amplifier, a gate which may beelectronic in nature, or even a relay, a time average integrating unit,and a comparator. The amplifier has an input which is the first variableto be multiplied as well as an output.

The time average integrating unit is electrically connected to theamplifier by way of the electronic gate or a relay gate contact, whichcontact is actuated by the relay gate armature which in turn iselectrically connected to the output of the amplifier. In the case of anelectronic gate the time average integrating unit is electricallycoupled to the output of the gate while the output from the amplifier isalso electrically coupled to the gate as an input.

The comparator has first and second inputs: the first input is areference signal which is an even valued periodic triangular function,and the second input is equal to the second variable.

In the case of an electronic gate the output from the comparator iselectrically coupled to the gate to thereby control delivery of theinput from the amplifier to the time average integrating unit.

In the case of a relay used as a gate the comparator has an output whichis electrically connected to the relay gate coil, which when energizedcauses the relay gate armature to close the relay gate contact. Thisenergization occurs only when the absolute value of the second variableis greater than the absolute value of the reference signal, thusproducing a signal on the comparator output. Accordingly, in either theelectronic gate embodiment or in the electro-mechanica1 relay situation,the time average integrating unit integrates the amplifier output toprovide the multiplication of the first and second variables.

The inventive concept can be extended to the multiplication of three ormore variable by use of a cascaded network technique which will beexplained more fully hereafter. Further, it should be noted thatalthough the foregoing description has been directed to a classificationyard environment, the present invention has a much wider scope inasmuchas it can be used wherever two or more variable must be multiplied.

Other objects and advantages of the present invention will becomeapparent from the ensuing description of illustration embodimentsthereof, in the course of which reference is had to the accompanyingdrawings in which:

FIG. 1 illustrates an analog multiplier of the prior art.

FIG. 2 illustrates the analog multiplier of the present invention inblock diagram form.

FIG. 2a depicts a diode bridge arrangement for deriving absolute valuesof incoming signals to the comparator of FIG. 2.

FIG. 3 depicts the analog multiplier of the present invention in partialblock diagram and circuit form. 7

FIG. 3a represents a signal from the output of the amplifier depicted inFIG. 2.

FIG. 3b represents a preferred waveform of the reference signal setforth in FIG. 2.

FIG. 30 sets forth the superimposed waveforms of the two inputs to thecomparator of FIG. 2.

FIG. 3d depicts a gate energization waveform over one cycle.

FIG. 3e represents the input signal to the time average integrating unitof FIG. 2.

FIG. 4 illustrates another embodiment of the present invention.

FIG. 5 illustrates an embodiment of the invention where themultiplication of three or more variables is accomplished by the use ofcascaded networks.

A description of the above embodiments will follow and then the novelfeatures of the invention will be presented in the appended claims.

Reference is now made to FIG. 1 in which is shown an analog multiplierof the prior art. A voltage X analogous to the first variable X which isto be multiplied is sent into a servo-motor 12 over lead 11. Thesenvo-motor 12 drives a shaft 13, the end of which carries a pinion 14which in turn drivingly engages a rack 14a. A rack and pinion arm 15secured to rack 14a, in this exemplary embodiment is electricallycoupled to a resilient lead 25, and may be in any of four positions 16,17, 18 or 19 (shown as broken lined arrows) depending upon the voltagelevel of the X voltage input. In FIG. 1, four discrete possible levelsare set forth for purposes of explanation only. The four voltage levelsare X =V =0; X =V X =V X =V =Y max., or the maximum voltage of thesecond variable Y. It should be noted that, while there are only fourlevels of the X input shown and four discrete positions of the rack andpinion arm 15 associated with the above-noted four voltage levels, theremay indeed be many more or less discrete voltage levels than that shownin FIG. 1.

As has been noted, the discrete voltage level of the X variable directlycontrols the rack and pinion 15 via servo-motor 21 such as to positionit along a potentiometer 20 which has a total resistance designated as Rand may be broken down into smaller resistances designated as r. Thevoltage between terminals A and B is the total voltage drop acrosspotentiometer 20 and is analogous to the second variable Y, i.e., Ylvolts is impressed on terminals A and B. For example, if

X: V =0 volts and X: V =2.5 volts and X=V :5.0 Volts and X: V =7.5 voltsthen the total voltage drop across the potentiometer 20 when the rackand pinion arm 15 is at position 19 would be Y volts, or the voltageimpressed on terminals A and B. If X is at the 5.0 voltage level, thenthe rack and pinion arm 15 would be positioned at position 18representative of a voltage drop of /3 Y volts. If the X voltage levelis at the 2.5 voltage level, then the rack and pinion arm 15 would beata voltage level indication which is shown by position 17 representativeof a voltage drop of /3 Y volts. If the X voltage level is at a zerolevel, then the rack and pinion arm 15 would be at position 16.

The potentiometer 20 is electrically connected to leads 21 and 22 vialeads 26 and 27, respectively. The lead 21 is electrically connected toan amplifier 23 whose gain is equal to Y max., the voltage analogous tothe maximum value of the second variable to be multiplied. Hence, if therange of X is from 0 to 7.5 volts and for the range for Y, 0 to 7.5volts, and X 2.5 volts while Y=3 volts, then the rack and pinion arm 15is at position 17 and the voltage carried on leads 21 and 25 toamplifier 23 is equal to /3 Y or 1 volt. The output of the amplifier 23is designated by the reference numeral 24 and is equal to 1 volt times Ymax., or 7.5 volts. As one experienced in the art can readily see, theoutput is indeed XY.

The maximum voltage drop across the potentiometer 20 cannot exceed themaximum voltage level presented by the X variable. In fact, Y max. mustequal the maximum voltage level presented by the variable X in volts.For if, using a similar example to that noted directly above, Y max.were set equal to 10 volts, while X max. remains 7.5 volts, X remains2.5 volts, and Y remains 3 volts, then the voltage carried on leads 21and 25 to amplifier 23 is equal to 1 volt, but the output of amplifier23, designated by the reference numeral 24 is equal to 1 volt times Ymax. or 10 volts, rather than 7.5 volts, which is the correct product.

As has been previously stated, the analog multiplier of the prior arthas disadvantages due to the mechanical movement of the rack and pinionarm 15 and also to the mechanical movement of the servo-motor 12. Inboth these mechanical movements, there is always present the possibilityof lost motion in the mechanism which inherently decreases the accuracyof the multiplier. Another disadvantage that is present in the analogmultiplier of the prior art is that it must contain limits on the twovariables to be multiplied. For example, the X variable can never exceedthe maximum value of the Y variable. To the problems noted above, theinvention to be described hereafter provides a solution which is new anddifferent.

Reference is now made to FIG. 2 which shows a block diagram of thepresent invention. An input X analogous to the first variable X to bemultiplied is sent into an amplifier 31 over lead 29. The amplifier 31is selected such that it has an output lead 32 on which appears theproduct XY max. and which it fed into gate 38. A reference voltage Ref.Y, which shall be described more fully hereinafter, is sent into acomparator 36, which has the ability to take absolute values of inputsignals and shall be described more fully hereafter, over lead 33, and aY voltage analogous to the second variable Y to be multiplied is sentinto the comparator 36 over lead 34. The output of the comparator ispresent on lead 37 and is sent into gate 38. The output of gate 38 issent into a time average integrating means 41 over lead 39. The timeaverage integrating means has an output 42 which would be the product ofX times Y.

The above-noted comparator 36 will be further described at this time.The comparator 36 only presents an output at lead 37 when the absolutevalue of the voltage Y is greater than the value of the reference signalvoltage Ref. Y. The reference signal voltage Ref. Y is an evenfunctioned periodic triangular signal and is normally positive. Inpractice this reference signal has the appearance of a sawtooth signal.

The comparator 36 has the ability, as forementioned, to take absolutevalues of incoming signals by use of a diode bridge arrangement which isincluded in comparator 36 and illustrated in FIG. 2a. In FIG. 2a asignal representative of the second variable Y is incoming on lead 34.If this signal is of the polarity plus to minus it will traverse acircuit from lead 102, to lead 103, through diode 104, lead 105,voltmeter 106, lead 105a, lead 107, diode 108, to lead 109 therebycausing voltmeter indicator 110 to deflect positively.

If an incoming signal is of the polarity, minus to plus, it willtraverse a circuit from lead 109 to lead 113, through diode 114, lead105, voltmeter 106, lead 105a, lead 111, diode 112, to lead 102, therebycausing voltmeter indicator 110 to once again deflect positively.

As is easily seen, the voltmeter indicator 110 always deflectspositively, i.e., the value of voltage visible on the voltmeter face andpresent on lead 115 is the absolute value of the incoming signal and thesignal on lead 115 delivers this absolute value to the conventionalcircuitry (not shown) of the comparator. It should be noted that whilethere is in FIG. 2a a diode bridge shown to take absolute values ofincoming signals, there may, indeed, be other ways of doing so, and thisspecific way is meant, by no means, to limit the present invention. Itshould also be noted that while the incoming signal of FIG. 2a is shownas the second variable Y, the diode bridge of the type shown in FIG. 2acould just as well be employed to handle the reference signal Y.Accordingly, a second diode bridge could be employed so that theabsolute values of both Y and Ref. Y may be derived and utilized in thecomparator 36. It should of course be recognized that the diode bridgeof FIG. 2a provides the multiplier of this invention with the ability tocope with the multiplication of minus numbers and in the absence of sucha requirement the diode bridge need not be included in the comparator36.

Reference is now made to FIG. 3 which depicts an analog multiplier ofthe present invention in which the gate 38 of FIG. 2 is in thisembodiment a relay 54. A voltage X analogous to the variable X which isthe first variable to be multiplied is sent over lead 46 into anamplifier 47. The waveform of the voltage X is shown by curve 77positioned immediately above the lead 46. As one can see, the voltage Xis a DC. voltage. For purposes of explanation only, X is shown as adiscrete steady state voltage. It is of course to be understood that Xmay vary. The amplifier is selected such that the output of theamplifier 47 is the product of X times Y max. which is present on lead48. The curve 78, depicted above the output lead 48, shows XY max. to bea DC. voltage, but at a higher value than the voltage X of curve 77.

A reference signal voltage Ref. Y is sent into a comparator 52 over lead49. The waveform of the reference 1 of the voltage Y is greater than theabsolute value of the reference voltage signal Ref. Y. When the relay 54is energized it closes a front contact a which thus completes a circuitfrom the lead 46 through amplifier 47, over lead 48, front contact a ofrelay 54, to a DArsonval voltmeter 56 which is a time averageintegrating voltmeter. The output of the DArsonval voltmeter 56 will bepresent on lead 57 and is the product employed of X times Y. It shouldbe noted that while a DArsonval voltmeter is shown as a time-averageintegrating means there may indeed be other conventional time-averageintegrating circuits.

A mathematical explanation of the attainmnet of the XY product presenton lead 57 will now be set forth by use of FIGS. 3a, 3b, 3c, 3d and 3e.

FIG. 3a once again depicts the voltage level at which XY max. is presentand which appears, for example, on lead 48 from amplifier 47 in FIG. 3.FIG. 3b depicts the waveform of the reference voltage signal Ref. Ywhich is present on lead 49 of FIG. 3. It can be seen that the maximumvalue of this voltage signal is selected to be Y max. FIG. 3c shows thewaveform of the variable voltage Y, which signal Y is superimposed onthe Waveform of the reference voltage signal Ref. Y. As one can easilysee, the absolute value of the voltage signal Y is greater than theabsolute value of the reference voltage signal Ref. Y from the origin,corresponding to time i=0 to point 43 on the triangular reference signalcurve corresponding to a time t The absolute value of the voltage signalY is less than the absolute value of the reference voltage signal Ref. Yfrom point 43 corresponding to a time t to point 44 on the triangularreference signal curve corresponding to a time t and the absolute valueof signal Y once again is greater than the absolute value of thereference voltage signal Ref. Y from point 44 corresponding to a time tto point 50 on the triangular reference signal curve corresponding to atime t However, since only one time period will be necessary for theintegration of the input to the time average integrating means 56 ofFIG. 3, we will only consider the period of time from point 44corresponding to a time t to a point 45 corresponding to a time t atwhich the absolute value of the voltage Y is greater than the absolutevalue of the reference Y voltage signal. This time period is designatedby the reference letter T in FIG. 30.

FIG. 3d shows a pulse train, the pulses indicative of the amount of timethat the relay 54 of FIG. 3 would be energized. For the period from 0 tot which is directly below the point 43 on curve of FIG. 3c, the relay 54will be energized since the absolute value of the voltage Y is indeedgreater than the absolute value of the reference signal voltage Ref. Y.For the time periods t to t the pulse will have died out and the voltagelevel will be at 0, since the absolute value of the reference voltagesignal Y is greater than the absolute value of the Y voltage signal. Andfrom time periods t to t the pulse will again appear since the absolutevalue of the reference Y voltage signal is less than the absolute valueof the Y voltage signal. Accordingly, observing FIG. 3e, one can seethat the output on the lead 48 of FIG. 3 will be gated to the DArsonvalvoltmeter 56 only at the times that the pulses in FIG. 3d are present.

A mathematical derivation of the time average integration of the wavefrom depicted in FIG. 3e will now be shown.

By use of similar triangles in FIG. 3c, specifically the smallertriangle bounded by the origin, point 43, and point 40 or time t and thelarger triangle bounded by the origin, point 60 and the point 58 or timeT/2, which is exactly equal to one-half of the period T, it is seenthat:

TY 2Y max.

and by use of similar triangles bounded by the origin, point 60, andpoint T 2, and point t point 44, and point i it is seen that:

Looking now at FIG. 3e, and taking a time-average integration over theperiod T it is seen that:

+f dt+f XY max. dz]

where {XY max.}(t) represents the product XY max. as a function of time.Making the proper substitutions, it is seen that T 2Y max.

T 2Y max. 2Y max. XY max. Y+2Y max.-2Y max.+Y T 2Y max.

=XY=integrated output on lead 57 of FIG. 3

2Y max.

Reference is now made to FIG. 4 in which is shown another embodiment ofthe present invention. A voltage X analogous to the variable X which isthe first variable to be multiplied is sent into an amplifier 62 overthe lead 61. The amplifier 62 has an output 63 on which is the productXY max. and which is electrically coupled to the source terminal 64 of afield effect transistor 70. A reference signal Ref. Y of the same typediscussed with reference to FIG. 3 is sent into comparator 68 over lead66 and a voltage Y analogous to the Y variable, which is the secondvariable to be multiplied is sent into comparator 68 over lead 67. Thecomparator 68 has an output 69 which is electrically coupled to the gateterminal 71 of the field effect transistor 70. The drain terminal 72 ofthe field effect transistor is electrically coupled to the lead 73 whichis input to the DArsonval voltmeter 74 which has an output 76 which isequivalent to the product XY. The field effect transistor 70 may be ann-channel junctional field elfect transistor such that whenever there isa positive voltage fed into the gate terminal 71 of the field effecttransistor 70, then an output will appear on the drain terminal 72 ofthe field effect transistor 70. It is therefore evident that themathematical interpretation of the embodiment presented in FIG. 4 wouldbe the same as o the mathematical interpretation presented by use ofFIGS. 3a, 3b, 3c, 3d and 3e above.

It should be noted that if either X or Y is negative then the amplifiershown in the general form as amplifier 31 in FIG. 2 would have an outputof XY max. and the mathematical derivation set forth heretofore would bethe same except that, now, XY max. would be substituted for XY max.

Reference is now made to FIG. 5 which is an embodiment of the inventionwhich is set forth should it be desired that three or more numbers bemultiplied. A voltage X analogous to the variable X which is the firstnumber to be multiplied is sent over lead 81 into an amplifier 82. Theoutput of the amplifier 82 is present on lead 83 and is XY max. Thereference signal voltage Ref. Y' is sent into a comparator 86 over lead84 and a Y signal voltage which is analogous to the second variable Y tobe multiplied is sent into the comparator 86 over lead 85. The output ofthe comparator is present on lead 87 and is present only when theabsolute value of the Y voltage is greater than the absolute value ofthe reference signal voltage Ref. Y as described above. Whenever thereis a voltage present on lead 87 from the comparator 86, a circuit iscompleted over lead 87 to a relay 88 to ground, thereby energizing relay88. When the relay 88 is energized it closes a front contact a whichcompletes a circuit from the lead 81 through amplifier 82 over lead 83,over front contact a of relay 88 to a DArsonval voltmeter 89 which hasan output 91 which is equivalent to the product XY.

This output product XY on lead 91 is fed into an amplifier 92. In thisembodiment Z is the third variable to be multiplied and Z max. is themaximum value the variable will attain. The output of the amplifier 92which is XYZ max. is present on lead 93. A reference Z voltage having amaximum value of Z max. is sent into a comparator 97 over lead 94 and aZ voltage which is analogous to the third variable Z to be multiplied issent into the comparator 97 over lead 96. The output of the comparatoris present on lead 98 only when the absolute value of the Z voltage isgreater than the absolute value of the reference voltage Ref. Z. Whenthis occurs a relay 99 is energized by the completion of a circuit fromthe comparator 97 through lead 98, through relay 99, to ground. Whenrelay 99 is energized a front contact a is closed, completing a circuitfrom lead 91 through amplifier 92, over front contact a of relay 99 to aDArsonval voltmeter 101 which has an output now of XYZ as shown byreference numeral 102 which may in turn be sent into another multiplyingcircuit similar to that of the one in FIG. 3 but not illustrated here.

While the invention has been shown and described with reference to aseries of preferred embodiments thereof, it will be understood by thoseskilled in the art that other modifications may be made therein withoutdeparting from the spirit and scope of the invention as is now set forthin the claims.

Having thus described my invention, what I claim is:

1. An improved analog multiplier for multiplying at least a first andsecond variable, said multiplier including in combination,

(a) amplifier means having an input which is said first variable as wellas an output, wherein said output of said amplifier means is equal tothe product of said first variable and a preselected gain of saidamplifier means, said preselected gain of said amplifier means having avalue at least equal to the maximum value of a reference signal,

(b) a gate,

(c) a time average integrating means, said amplifier means outputelectrically coupled to said time average integrating means by way ofsaid gate,

(d) comparator means having first and second inputs, said first inputbeing said reference signal and said second input being said secondvariable, said comparator means having an output which controls saidgate whenever a signal appears on said comparator output to allow saidtime average integrating means to integrate said output from saidamplifying means to provide multiplication of said first and said secondvariables independent of said reference signal, said comparator outputsignal appearing only when the absolute value of said second variable isgreater than the absolute value of said reference signal.

2. The analog multiplier of claim 1 wherein said comparator includesmeans to determine the absolute value of both said reference signal andsaid second variable.

3. The analog multiplier of claim 1 wherein said gate is a field effecttransistor which has its gate terminal electrically connected to saidoutput of said comparator means and its source terminal electricallyconnected to said output of said amplifying means and its drain terminalelectrically connected to said time average integrating means.

4. The analog multiplier of claim 1 wherein said gate is a relay whichhas its coil electrically connected to said output of said comparatormeans and its armature electrically connected to said output of saidamplifying means and a contact electrically connected to said timeaverage integrating means.

5. The analog multiplier of claim 1 wherein said reference signal is aperiodic signal being an even valued linear function.

6. The analog multiplier of claim 5 wherein said reference signal has anabsolute maximum value equal to at least the maximum absolute value ofsaid second variable.

7. The analog multiplier of claim 1 wherein said time averageintegrating means is a DArsonval voltmeter.

8. An improved analog multiplier for multiplying at least a first andsecond variable and third variable, said multiplier including incombination,

(a) a first amplifier means having an input which is said first variableas well as an output, wherein said output of said first amplifier meansis equal tothe product of said first variable and a preselected gain ofsaid first amplifier means, said preselected gain of said firstamplifier means having a value equal to at least the maximum value of afirst reference signal,

(b) a first gate,

(0) a first time average integrating means, said first ampliying meansoutput electrically coupled to said first time average integrating meansby way of said first gate,

(d) first comparator means having first and second inputs, said firstinput being said first reference signal and said second input being saidsecond variable, said first comparator means having an output whichcontrols said first gate whenever a signal appears on said firstcomparator output to allow said first time average integrating means tointegrate said output from said first amplifying means to providemultiplication of said first and said second variables independent ofsaid first reference signal, said first comparator output signalappearing only when the absolute value of said second variable isgreater than the absolute value of said reference signal,

(e) said first time average integrating means having an output which isthe product of said first and said second variable,

said output from said first time average integrating means coupled tothird variable multiplying means.

9.-The analog multiplier of claim 8 wherein said third variablemultiplying means includes (a) a second amplifier means having an inputwhich is said product of said first and second variables as well as anoutput, whereinsaid output of said second amplifier means is equal tothe product of said first variable, said second variable, and apreselected gain of said second amplifier means, said preselected gainof said second amplifier means having a value equal to at least themaximum value of a second reference signal,

(b) a second gate,

(c) a second time average integrating means, said second amplifyingmeans output electrically coupled to said second time averageintegrating means by way of said second gate,

(d) a second comparator means having first and second inputs, said firstinput being said second reference signal and said second input beingsaid third variable, said second comparator means having an output whichcontrols said second gate whenever a signal appears on said secondcomparator output to allow said second time average integrating means tointegrate said output from said second amplifying means to providemultiplication of said first and said second variables and thirdvariable independent of said first and second reference signals, saidsecond comparator output appearing only when the absolute value of saidthird variable is greater than the absolute value of said secondreference signal.

10. The analog multiplier of claim 9 wherein said first and said secondreference signals respectively have absolute maximum values equal to atleast the maximum absolute values of said second variable and said thirdvariable.

References Cited UNITED STATES PATENTS EUGENE G. BOTZ, Primary ExaminerJ. F. RUGGIERO, Assistant Examiner US. Cl. X.R. 235-l83

